Problem: Solve for $x$ and $y$ using elimination. ${-x-6y = -19}$ ${x-5y = -3}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-11y = -22$ $\dfrac{-11y}{{-11}} = \dfrac{-22}{{-11}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {-x-6y = -19}\thinspace$ to find $x$ ${-x - 6}{(2)}{= -19}$ $-x-12 = -19$ $-x-12{+12} = -19{+12}$ $-x = -7$ $\dfrac{-x}{{-1}} = \dfrac{-7}{{-1}}$ ${x = 7}$ You can also plug ${y = 2}$ into $\thinspace {x-5y = -3}\thinspace$ and get the same answer for $x$ : ${x - 5}{(2)}{= -3}$ ${x = 7}$